Analysis of degradation data of poly(l-lactide-co-l,d-lactide) and poly(l-lactide) obtained at elevated and physiological temperatures using mathematical models

An integrated mechanical degradation model to explore the mechanical response of a bioresorbable polymeric scaffold

Simulation of bioresorbable medical devices is hindered by the limitations of current material models. Useful simulations require that both the short- and long-term response must be considered; existing models are not physically-based and provide limited insight to guide performance improvements. This study presents an integrated degradation framework which couples a physically-based degradation model, which predicts changes in both crystallinity (Xc) and molecular weight (Mn), with the results of a micromechanical model, which predicts the effective properties of the semicrystalline polymer. This degradation framework is used to simulate the deployment of a bioresorbable PLLA (Poly (L-lactide) stent into a mock vessel and the subsequent mechanical response during degradation under different diffusion boundary conditions representing neointimal growth. A workflow is established in a commercial finite element code that couples both the immediate and long-term responses. Clinically relevant lumen loss is reported and used to compare different responses and the effect of neo-intimal tissue regrowth post-implantation on degradation and on the mechanical response is assessed. In addition, the effects of possible changes in Xc, which could occur during processing and stent deployment, are explored.

Mechanistic Computational Modeling of Implantable, Bioresorbable Drug Release Systems

Implantable, bioresorbable drug delivery systems offer an alternative to current drug administration techniques; allowing for patient-tailored drug dosage, while also increasing patient compliance. Mechanistic mathematical modeling allows for the acceleration of the design of the release systems, and for prediction of physical anomalies that are not intuitive and may otherwise elude discovery. This study investigates short-term drug release as a function of water-mediated polymer phase inversion into a solid depot within hours to days, as well as long-term hydrolysis-mediated degradation and erosion of the implant over the next few weeks. Finite difference methods are used to model spatial and temporal changes in polymer phase inversion, solidification, and hydrolysis. Modeling reveals the impact of non-uniform drug distribution, production and transport of H+ ions, and localized polymer degradation on the diffusion of water, drug, and hydrolyzed polymer byproducts. Compared to experimental data, the computational model accurately predicts the drug release during the solidification of implants over days and drug release profiles over weeks from microspheres and implants. This work offers new insight into the impact of various parameters on drug release profiles, and is a new tool to accelerate the design process for release systems to meet a patient specific clinical need.

A reaction-diffusion framework for hydrolytic degradation of amorphous polymers based on a discrete chain scission model

Hydrolytic degradation of polymers involves the scission of long chain molecules, leading to molecular weight reduction and mass loss. The precise degradation response however depends on the scission probability of individual bonds along the polymer backbone. In particular, bonds near the chain ends are considered to be more susceptible to hydrolysis than inner bonds. In this paper, we incorporate a discrete chain scission model that can handle arbitrary bond scission probabilities within a continuum reaction-diffusion framework. Overall hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. By decoupling the description of the chain scission mechanism from kinetics, our framework enables the identification of the chain scission mechanism from molecular weight reduction and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations while retaining the predictive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. STATEMENT OF SIGNIFICANCE: Many models have been proposed to predict the evolution of molecular weight and mass loss in biodegradable polymers undergoing hydrolytic degradation. However, existing models remain limited in their ability to describe the degradation mechanism, autocatalytic kinetics and short chains diffusion simultaneously. Moreover, existing models often rely on empirical relations and a large number of fitting parameters. Here, we propose a conceptually simple discrete-continuum mathematical framework with a small number of parameters which all have a clear physical meaning. Model calibration against experimental data is simplified, and further provides insights into the degradation mechanisms at play, namely random scission, chain-end scission, or a combination of both. The framework can serve as a basis for future generalisations, including a description of evolving crystallinity, or other degradation mechanisms, such as thermal oxidation or photo-degradation.

A Computational Model for the Release of Bioactive Molecules by the Hydrolytic Degradation of a Functionalized Polyester-Based Scaffold

This work presents a computational model to study the degradation behavior of polyester-based three-dimensional (3D) functionalized scaffolds for bone regeneration. As a case study, we investigated the behavior of a 3D-printed scaffold presenting a functionalized surface with ICOS-Fc, a bioactive protein able to stimulate bone regeneration and healing, inhibiting osteoclast activity. The aim of the model was to optimize the scaffold design to control its degradation and thus the release of grafted protein over time and space. Two different scenarios were considered: (i) a scaffold without macroporosity presenting a functionalized external surface; and (ii) a scaffold presenting an internal functionalized macroporous architecture with open channels to locally deliver the degradation products.

Angiogenic Modification of Microfibrous Polycaprolactone by pCMV-VEGF165 Plasmid Promotes Local Vascular Growth after Implantation in Rats

Insufficient vascular growth in the area of artificial-material implantation contributes to ischemia, fibrosis, the development of bacterial infections, and tissue necrosis around the graft. The purpose of this study was to evaluate angiogenesis after implantation of polycaprolactone microfiber scaffolds modified by a pCMV-VEGF165-plasmid in rats. Influence of vascularization on scaffold degradation was also examined. We investigated flat microfibrous scaffolds obtained by electrospinning polycaprolactone with incorporation of the pCMV-VEGF-165 plasmid into the microfibers at concentrations of 0.005 ng of plasmid per 1 mg of polycaprolactone (0.005 ng/mg) (LCGroup) and 0.05 ng/mg (HCGroup). The samples were subcutaneously implanted in the interscapular area of rats. On days 7, 16, 33, 46, and 64, the scaffolds were removed, and a histological study with a morphometric evaluation of the density and diameter of the vessels and microfiber diameter was performed. The number of vessels was increased in all groups, as well as the resorption of the scaffold. On day 33, the vascular density in the HCGroup was 42% higher compared to the control group (p = 0.0344). The dose-dependent effect of the pCMV-VEGF165-plasmid was confirmed by enhanced angiogenesis in the HCGroup compared to the LCGroup on day 33 (p-value = 0.0259). We did not find a statistically significant correlation between scaffold degradation rate and vessel growth (the Pearson correlation coefficient was ρ = 0.20, p-value = 0.6134). Functionalization of polycaprolactone by incorporation of the pCMV-VEGF165 plasmid provided improved vascularization within 33 days after implantation, however, vessel growth did not seem to correlate with scaffold degradation rate.

Enhanced Polyester Degradation through Transesterification with Salicylates

Polyesters constitute nearly 10% of the global plastic market, but most are essentially non-degradable under ambient conditions or in engineered environments. A range of degradable polyesters have been developed as more sustainable alternatives; however, limitations of practical degradability and scalability have hindered their viability. Here, we utilized transesterification approaches, including in situ polymerization-transesterification, between a salicylate and a polyester to incorporate salicylate units into commercial polyester backbones. The strategy is scalable and practically relevant given that high molar mass polymers can be obtained from melt-processing of commercial polyesters using common compounders or extruders. Polylactide containing sparse salicylate moieties shows enhanced hydrolytic degradability in aqueous buffer, seawater, and alkaline solutions without sacrificing the thermal, mechanical, and O₂ barrier properties of the parent material. Additionally, salicylate sequences were incorporated into polycaprolactone and a derivative of poly(ethylene terephthalate), and those modified polymers also exhibited facile degradation behavior in alkaline solution, further expanding the scope of this approach. This work provides insights and direction for the development of high-performance yet more sustainable and degradable alternatives to conventional polyesters.

Surface Engineering of Cardiovascular Devices for Improved Hemocompatibility and Rapid Endothelialization

Cardiovascular devices have been widely applied in the clinical treatment of cardiovascular diseases. However, poor hemocompatibility and slow endothelialization on their surface still exist. Numerous surface engineering strategies have mainly sought to modify the device surface through physical, chemical, and biological approaches to improve surface hemocompatibility and endothelialization. The alteration of physical characteristics and pattern topographies brings some hopeful outcomes and plays a notable role in this respect. The chemical and biological approaches can provide potential signs of success in the endothelialization of vascular device surfaces. They usually involve therapeutic drugs, specific peptides, adhesive proteins, antibodies, growth factors and nitric oxide (NO) donors. The gene engineering can enhance the proliferation, growth, and migration of vascular cells, thus boosting the endothelialization. In this review, the surface engineering strategies are highlighted and summarized to improve hemocompatibility and rapid endothelialization on the cardiovascular devices. The potential outlook is also briefly discussed to help guide endothelialization strategies and inspire further innovations. It is hoped that this review can assist with the surface engineering of cardiovascular devices and promote future advancements in this emerging research field.

Simulations of the Biodegradation of Citrate-Based Polymers for Artificial Scaffolds Using Accelerated Reactive Molecular Dynamics

In this study, we investigate the reactivity and mechanical properties of poly(1,6-hexanediol-co-citric acid) via ReaxFF molecular dynamics simulations. We implement an accelerated scheme within the ReaxFF framework to study the hydrolysis reaction of the polymer which is provided with a sufficient amount of energy known as the restrain energy after a suitable pretransition-state configuration is obtained to overcome the activation energy barrier and the desired product is obtained. The validity of the ReaxFF force field is established by comparing the ReaxFF energy barriers of ester and ether hydrolysis with benchmark DFT values in the literature. We perform chemical and mechanical degradation of polymer chain bundles at 300 K. We find that ester hydrolyzes faster than ether because of the lower activation energy barrier of the reaction. The selectivity of the bond-boost scheme has been demonstrated by lowering the boost parameters of the accelerated simulation, which almost stops the ether hydrolysis. Mechanical degradation of prehydrolyzed and intermittent hydrolyzed polymer bundles is performed along the longitudinal direction at two different strain rates. We find that the tensile modulus of the polymers increases with increase in strain rates, which shows that polymers show a strain-dependent behavior. The tensile modulus of the polyester-ether is higher than polyester but reaches yield stress faster than polyester. This makes polyester more ductile than polyester-ether.

Co-existence effect of tricalcium phosphate and bioactive glass on biological and biodegradation characteristic of Poly L-Lactic Acid (PLLA) in trinary composite scaffold form

The purpose of this study is to analyze the co-existence effect of 30 wt.% TCP-BG phases on degradation and precipitation behaviors of PLLA based composite scaffold in biological media. First, phase separation method was used to synthesize of the pure PLLA and the trinary composite scaffolds, and second they were immersed in SBF solution for 45 days. Subsequently, the degradation and precipitation characteristic were investigated by analyzing of pH value and weight changes of the immersed samples, the ability of biological products formation and the change of relative molecular weight of PLLA matrix as function of the degradation time. Finally, the experimental data of relative molecular weight change were verified by Han and Pan model and comparisons were made between them. Results have represented precipitation of huge amount of carbonate apatite on surface of the composite scaffold, and also the acidity of SBF media changes moderately which is prove better bioactivity properties compare to the pure PLLA scaffold. The results of comparison with the model point to quiet good agreement between them in early stage of degradation. So, the consequences suggest that the TCP-BG/PLLA composite scaffold have great potential to be applied in bone replacements or repairs.

Modeling of Biodegradable Polyesters With Applications to Coronary Stents

The interest in biodegradable polymers for clinical and biomedical engineering applications has seen a dramatic increase in the last 10 years. Recent innovations include bioresorbable polymeric stents (BPS), which are temporary vascular scaffolds designed to restore patency and provide short-term support to a blocked blood vessel, before becoming naturally resorbed over time. BPS offer possibilities to overcome the long-term complications often observed with the permanent metallic stents, well established in the treatment of coronary and peripheral artery disease. From the perspective of designing next generation BPS, the bulk degradation behavior of the polymer material adds considerable complications. Computational modeling offers an efficient framework to predict and provide understanding into the behavior of medical devices and implants. Current computational modeling techniques for the degradation of BPS are either phenomenologically or physically based. In this work, a physically based polymer degradation model is implemented into a number of different computational frameworks to investigate the degradation of a number of polymeric structures. A thermal analogy is presented to implement the degradation model into the commercially available finite-element code, abaqus/standard. This approach is then applied to the degradation of BPS, and the effects of material, boundary condition, and design on the degradation rates of the stents are examined. The results indicate that there is a notable difference in the molecular weight trends predicted for the different materials and boundary condition assumptions investigated, with autocatalysis emerging as a dominant mechanism controlling the degradation behavior. Insights into the scaffolding ability of the various BPS examined are then obtained using a suggested general relationship between Young's modulus and molecular weight.

Degradation mechanisms of bioresorbable polyesters. Part 1. Effects of random scission, end scission and autocatalysis

A mathematical model was developed to relate the degradation trend of bioresorbable polymers to different underlying hydrolysis mechanisms, including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. The effect of each mechanism on molecular weight degradation and potential mass loss was analysed. A simple scheme was developed to identify the most likely hydrolysis mechanism based on experimental data. The scheme was first demonstrated using case studies, then used to evaluate data collected from 31 publications in the literature to identify the dominant hydrolysis mechanisms for typical biodegradable polymers. The analysis showed that most of the experimental data indicates autocatalytic hydrolysis, as expected. However, the study shows that the existing understanding on whether random or end scission controls degradation is inappropriate. It was revealed that pure end scission cannot explain the observed trend in molecular weight reduction because end scission would be too slow to reduce the average molecular weight. On the other hand, pure random scission cannot explain the observed trend in mass loss because too few oligomers would be available to diffuse out of a device. It is concluded that the chain ends are more susceptible to cleavage, which produces most of the oligomers leading to mass loss. However, it is random scission that dominates the reduction in molecular weight.

Degradation mechanisms of bioresorbable polyesters. Part 2. Effects of initial molecular weight and residual monomer

This paper presents an understanding of how initial molecular weight and initial monomer fraction affect the degradation of bioresorbable polymers in terms of the underlying hydrolysis mechanisms. A mathematical model was used to analyse the effects of initial molecular weight for various hydrolysis mechanisms including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. Different behaviours were identified to relate initial molecular weight to the molecular weight half-life and to the time until the onset of mass loss. The behaviours were validated by fitting the model to experimental data for molecular weight reduction and mass loss of samples with different initial molecular weights. Several publications that consider initial molecular weight were reviewed. The effect of residual monomer on degradation was also analysed, and shown to accelerate the reduction of molecular weight and mass loss. An inverse square root law relationship was found between molecular weight half-life and initial monomer fraction for autocatalytic hydrolysis. The relationship was tested by fitting the model to experimental data with various residual monomer contents.

In vitro characteristics of a gelling PEGDA-QT polymer system with model drug release for cerebral aneurysm embolization

A liquid-to-solid gelling polymer system, such as the poly(ethylene glycol) diacrylate-pentaerythritol tetrakis (3-mercaptopropionate) (PEGDA-QT) system, can fill cerebral aneurysms more completely than current embolization materials, reducing the likelihood of aneurysm recurrence. PEGDA-QT gels were formulated using PEGDA of different molecular weights (PEGDA575 and PEGDA700 ), and their characteristics were examined in vitro. Experiments examined gel time, mass change, crosslink integrity, cytotoxicity, and protein release capabilities. In general, PEGDA575 -QT gels were more hydrophobic, requiring an initiating solution with a higher pH (pH 9.5) to achieve a gel time comparable to PEGDA700 -QT gels, which used an initiating solution at pH 9.19. The mass change and crosslink integrity of gels were analyzed over time after gels were submerged in 150 mM phosphate buffered saline. After 380 days, PEGDA575 -QT gels achieved a maximum mass increase of 72% due to water uptake, while PEGDA700 -QT gels doubled their initial mass (100% increase) by 165 days. Compression tests showed that PEGDA700 -QT gels hydrolyzed more quickly than PEGDA575 -QT gels. Cytotoxicity assays showed that in general, PEGDA575 -QT negatively affected cell growth, while PEGDA700 -QT gels promoted cell viability. Sustained, controlled release of lysozyme, a 14.3 kDa protein, was achieved over an 8-week period when loaded into PEGDA700 -QT gels, but PEGDA575 -QT gels did not show sustained release. These studies show that although they are similar in composition, these PEGDA-QT gel formulations behave considerably differently. Although PEGDA700 -QT gels swell more and degrade faster than PEGDA575 -QT gels, their cytocompatibility and protein release characteristics may prove to be more beneficial for in vivo aneurysm treatment. © 2013 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2013.

Polymer chain scission, oligomer production and diffusion: a two-scale model for degradation of bioresorbable polyesters

This paper presents a computer model for the biodegradation of polyesters such as poly(lactic acid), poly(glycolic acid) and their copolymers. The model can take polymer details such as molecular weight distribution, different end and random scission rates and copolymer ratio as input data. A multi-scale approach is developed: polymer chain scission and oligomer production which occur at the molecular scale are modelled using a kinetic Monte Carlo scheme, oligomer diffusion which occurs at the device scale is modelled using a diffusion equation, and the two are connected at the finite difference nodes of the diffusion equation. The two-scale model can be used to predict the temporal evolution and spatial distribution of molecular weight distribution in a device as well as the weight loss as a function of time. It is shown that the kinetic Monte Carlo scheme can accurately predict the effect of copolymer ratio on the degradation rate. Grizzi and co-workers observed in their experiments that a PLA film 0.3mm thick degrades much more slowly than one that is 2mm thick. The numerical study shows that the conceptional reaction diffusion model suggested by Grizzi et al. needs to be extended in order to explain the size effect fully.